Stefan Weinzierl - Feynman Integrals : A Comprehensive Treatment for Students and Researchers

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UNITEXT for Physics

Series Editors

Michele Cini

University of Rome Tor Vergata, Roma, Italy

Attilio Ferrari

University of Turin, Turin, Italy

Stefano Forte

University of Milan, Milan, Italy

Guido Montagna

University of Pavia, Pavia, Italy

Oreste Nicrosini

University of Pavia, Pavia, Italy

Luca Peliti

University of Napoli, Naples, Italy

Alberto Rotondi

Pavia, Italy

Paolo Biscari

Politecnico di Milano, Milan, Italy

Nicola Manini

University of Milan, Milan, Italy

Morten Hjorth-Jensen

University of Oslo, Oslo, Norway

UNITEXT for Physics series publishes textbooks in physics and astronomy, characterized by a didactic style and comprehensiveness. The books are addressed to upper-undergraduate and graduate students, but also to scientists and researchers as important resources for their education, knowledge, and teaching.

More information about this series at https://link.springer.com/bookseries/13351

Stefan Weinzierl

Feynman Integrals

A Comprehensive Treatment for Students and Researchers

Logo of the publisher

Stefan Weinzierl

Institut fr Physik, Universitt Mainz, Mainz, Rheinland-Pfalz, Germany

ISSN 2198-7882 e-ISSN 2198-7890

UNITEXT for Physics

ISBN 978-3-030-99557-7 e-ISBN 978-3-030-99558-4

https://doi.org/10.1007/978-3-030-99558-4

The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AG

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Symbols

Feynman parameter

Schwinger parameter

Baikov polynomial

c

Speed of light

D

Dimension of space-time

Dint

(integer) expansion point within dimensional regularisation

Dimensional regularisation parameter

Second Symanzik polynomial

Lee-Pomeransky polynomial

E

Euler-Mascheroni constant

Grp

Category of groups

Reduced Planck constant

Hom

Morphisms of a category

HS

Category of (pure) Hodge structures

Kirchhoff polynomial

l

Loop number

MHS

Category of mixed Hodge structures

MixMot

Category of mixed motives

ModR

Category of finitely generated R-modules

n

Number of edges

NB

Number of kinematic variables

Ncohom

Dimension of the twisted cohomology group

next

Number of external edges

nint

Number of internal edges

NL

Number of letters

Nmaster

Number of master integrals

NV

Number of Baikov variables

Obj

Objects of a category

ProjR

Category of finitely generated projective R-modules

PureMot

Category of pure motives

r

Number of vertices

rint

Number of internal vertices

Set

Nategory of sets

Category of smooth projective varieties over

First Symanzik polynomial

uj

Lee-Pomeransky variable

Category of algebraic varieties defined over

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